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**Cost-benefit analysis in Disaster Risk Management**

Cees van Westen

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**Disaster Risk Management**

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Risk Evaluation. Risk evaluation is the stage at which values and judgment enter the decision process, explicitly or implicitly, by including consideration of the importance of the estimated risks and the associated social, environmental, and economic consequences, in order to identify a range of alternatives for managing the risks. We have analyzed the risk either qualitatively or quantitatively. Now questions arise: Is the risk too high? Where is the risk too high? What is too high? What do the people think?

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**Risk evaluation versus perception**

Risks can classified into involuntary risk and voluntary risks. Risks associated with natural hazards are often classified as involuntary risk. They often relate to rare events with catastrophic potential impacts. Lay perceivers (or non-experts) give more weight to hazards that take many lives at ones that is to major disasters ( Smith, 2001). Technical experts assess infrequent hazards that take many lives at one time equal to regular hazards that take a similar number of lives just once in a time (over an equivalent period) ( Smith, 2001).

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Two dimensions of risk The “factual” dimension, which indicates the actual measured level of risk, and which can be expressed in probability of losses (e.g. number of people, building, monetary values) The “socio-cultural” dimension, which includes how a particular risk is viewed when values and emotions come into play.

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Risk perception Risk perception is the way how people/communities/authorities judge the severity of the risk. Do they know? Are they worried? Are they prepared to act? Who they think should act? What is it worth to them?

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**Factors that determine risk perception**

Their personal situation. Cultural and religious background. Social background Economic level Political background Level of awareness Media exposure Other risks Risk reduction situation Acceptable risk: a risk which the society or impacted individuals are prepared to accept. Actions to further reduce such risk are usually not required unless reasonably practicable measures are available at low cost in terms of money, time and effort. Tolerable risk: a risk within a range that society can live with so as to secure certain net benefits. It is a range of risk regarded as non-negligible and needing to be kept under review and reduced further if possible. ALARP (As Low As Reasonably Practicable) principle: Principle which states that risks, lower than the limit of tolerability, are tolerable only if risk reduction is impracticable or if its cost is grossly in disproportion (depending on the level of risk) to the improvement gained.

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Risk evaluation. The ALARP principle is that the residual risk shall be as low as reasonably practicable. Must be avoided or reduced; Risk reduction cost may be taken into account. Beyond a certain point investment in RR may be inefficient.

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**Risk evaluation based on F-N curves**

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**Which risk is acceptable?**

During the life of an average person, the chance of death is never less than 1:10,000 (1.000E-4): this is due to all causes. So it would not be realistic to require the risk due to natural disasters to be lower than this. These curves differ from country to country. No international standards Voluntary – involuntary risk is also relevant.

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F-N curves Risk acceptability is mostly defined on the basis of F-N curves

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**Risk acceptance criteria in Netherlands**

“dyke rings” that protect a part of the country against flooding. The more important the area, the lower the chance that the dyke ring breaks and the area will be flooded.

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**Cost- benefit analysis**

An important aspect in risk evaluation is also: How much do we need to spend in order to reduce the risk Benefits Costs

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**Tools to evaluate best risk reduction measures**

Cost Benefit Analysis (CBA) is used to compare costs and benefits of a one specific measures or a set of alternative measures over a period of time for a. CBA assesses the measure(s) mainly on the basis of the efficiency criterion. It requires the monetization of all the effects. The effects that cannot be expressed in monetary terms will be usually described in their original unit of measurement. Cost Effectiveness Analysis: (CEA) has most of the features of CBA, but does not require the monetization of either the benefits or the costs (usually the benefits). CEA does not show whether the benefits outweigh the costs, but shows which alternative has the lowest costs (with the same level of benefits). CEA is often applied when the norm for a certain level of safety has been set. CEA analyzes which types of solution is the ‘cheapest’ given a certain level of safety standard. Multi Criteria Analysis (MCE) is a tool that allows comparing alternative measures on multiple criteria. In contrast to CBA, MCE allows the treatment of more than one criterion and does not require the monetization of all the impacts. MCE results in a ranking of alternatives.

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**c. Which alternative is economically the most attractive?**

If all alternatives are all as effective in terms of risk reduction the cheapest alternative (Cost Effectiveness Analysis, CEA) If effectiveness in risk reduction differs the cheapest alternative in terms of risk reduced (Cost Benefit Analysis, CBA) Flood proofing relocation. Levees

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**What is an optimal level of a risk reducing measure?**

A number (most?) risk reduction measures could be applied in a variable way Height level of dikes Earthquake resistance of buildings Legal restrictions land use ….. A higher level of risk reducing measures reduced risk, BUT diminishing returns Often at higher variable costs MORE is not necessarily more beneficial EXAMPLE: small example CBA_risk_reducing

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**Cost-Benefit Analysis and Damage Assessment – for whom??**

Government and funding agencies National and provincial governments Governments/general public Emergency planners Insurance companies Private firms/house owners Ex-ante project appraisal Accountability - Tax money Economic loss - compensation Identification of critical risk areas Financial loss Insurance or other protection measures

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**Perspective – damage/cost/benefits for whom?**

Public: national ministries, provincial governments, emergency planners Private: private firms, private property owners, insurance companies Economic values – real values – broad economic perspective Financial values – monetary values

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**Cost Benefit Analysis of Risk Reducing Measures**

Costs for (structural) risk reducing measures are relatively less difficult to estimate Estimating the benefits is a major challenge ! We need to know: Avoided damage Probability of damage We need to estimate: how often natural hazard events occur (frequency) how much damage and losses occur as a result of the event

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**Do we include all losses?**

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**Costs of Natural Hazards - e.g. flooding**

Indirect damage income forgone interruption of economic and social activities extra costs of transportation due to infrastructure damage Direct damage buildings infrastructure crops and livestock Machines human victims landscape/nature

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**Damage functions Damage-probability curve Damage-probability curve**

in case of flood protection against events upto 1:100 years

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**Basic CBA steps Define scope of the project**

Identify the type of costs and benefits Put monetary values on costs and benefits Compare costs and benefits Calculate profitability indicators/decision criteria Sensitivity analysis Make recommendations

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**What do we need to know of both scenarios?**

The costs of both scenarios (investment and annual) The investment period The benefits (i.e. annual risk reduction) of both scenarios The life time of the investment Discount rate

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**Cost benefit analysis Calculate economic risk**

Define risk reduction measures Define cost of risk reduction measures Define characteristics Analyze cost benefits

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**Calculating economic losses**

First we will calculate the total floorspace within each mapping unit. We do this by multiplying the building footprint area with the number of floors. Then we use unit costs (per square meter) per urban landuse type for buildings and for contents of buildings. We multiply these with the floorspace to get the total costs per mapping units. Then we will generate attribute maps that contain the costs of buildings affected for each hazard type and hazard class. We will then use the results from the annual loss estimation to combine these with the vulnerability and probability if these are not yet included. We will then combine the data and generate risk curves.

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Economic risk

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**Risk reduction measures**

The municipality of RiskCity has made a study and the report came up with the following possibilities for risk reduction. The following table shows a number of possible risk reduction measures, including also a very general indication of the costs that these measures would take. In the following section we will evaluate some of these in more detail.

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**Example CBA Flood Reducing Measures**

Scenario I (removal) removal of housing in the 10-year Return Period flood zone 10 year RP flood zone is converted into green areas buildings are demolished, new terrain to be bought, and new buildings have to be constructed in other hazard free zones the set-up of a vigilance group is required The risk in the area that was formerly threatened by a 10 year Return Period flood will be reduced to 0 Scenario II (retention) construction of an upstream storage lake engineering works flood retention basin and drainage need maintenance the retention basin will reduce the flood losses. It will retain the discharge for 2 and 5 years RP and reduce the risk to 0. For the other return periods the damage will reduce the losses

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**Damage without risk reduction, Scenario I and II at different Return Periods**

Flooding Return Period Annual Probability without mitigation Scenario 1 Scenario 2 2 0.5 0.0 5 0.2 19.3 10 0.1 34.4 25 0.04 100.0 65.6 50 0.02 199.0 164.6 100 0.01 510.0 475.6 200 0.005 1134.0 1099.6

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**3. Annual risk reduction of both scenarios**

Costs Scenario I (removal) Costs Scenario II (retention)

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**Triangles and rectangles method**

This is the annual risk, taking the sum of the triangles and squares in the graph Triangles and rectangles method The area under the curve is divided into trangles, which connect the straight lines between two points in the curve and have X-axis difference as difference between the losses of the two scenarios. Y-axis of the triangles is the difference in probability between two scenarios. The remaining part under the curve is then filled up with rectangles, as illustrated in the graph and table below.

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**Simplified rectangles method**

In this method we simplify the graph into a number of rectangles, which have as Y-axis the difference between two successive scenarios, and as X-axis the average losses between two successive loss events. See graph and Excel table below

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Risk reduction Now that we have calculated the annual loss for the existing situation, we can also now evaluate the reduction in total annual losses for the two scenarios. Calculate in Excel in the same way the average annual risk for Scenario I and Scenario II ( see earlier table with the losses for the two scenarios for the various return periods that you filled in yourself) Calculate the amount of risk reduction, comparing Scenario 1 and Scenario 2 with the original average annual risk. Fill in the table below.

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**Calculating the investment costs**

After calculating how much the risk reduction is on an annual basis for the two different scenarios, we can now evaluate the benefits. The benefit is equal to the amount of risk reduction. However, the two risk reduction scenarios also involve certain costs. The next table indicates the investment costs for implementing the two scenarios.

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Calculate costs To calculate the A to D component costs from the table above, you need to know first the number of buildings in the flood zone of 10 years return period. For the component E you need to know the area pf the 10 year flood zone.

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Costs After calculating the risk reduction (benefit) and the investment costs of the two flood scenarios we can now continue to evaluate the cost/benfits. The following table indicates the costs of the two scenarios.

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**Maintenance and operation costs**

Each of the two scenarios will also require long term investments. Scenario 1 requires the set-up of a municipal organization that controls the illegal spread of housing in highly hazardous areas. It will require staff, office and equipment costs, which will rise over time depending on the increases of salary and inflation. The annual costs are estimated to be We consider that these costs will increase with 5 % each year. Scenario 2 also requires maintenance and operation costs. The flood retention basin contains a basin in which sediments are deposited. Annually the sediments from this basin have to be removed using heavy equipment. Also the drainage works needs regular repair. The costs for maintenance are considered to be per year. We consider that these costs will increase with 5 % each year. See table below.

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Investment period The investments for both scenarios are not done within one single year. They are spread out over a larger number of years, because normally not all activities can be carried out in the same year. It is quite difficult to remove existing buildings. The municipality would like to buy the land of private owners, but they will resist, and there will be many lawsuits that might take a lot of time. Therefore we consider that the entire relocation of all building might take as much as 10 years. The investment costs are therefore spread out over this period. The construction of the engineering works for scenario 2 will take less time. Still it is considered that the costs are spread over a period of 3 years. The benefits will start in the year that the investments are finished. For scenario 1 this is in year 11 and for scenario 2 it is in year 4.

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Project lifetime The lifetime of the scenario 2 is considered to be 40 year. After that the structure will have deteriorated and it needs to be rebuilt. For the relocation scenario it is more difficult to speak about a life time, but we will also keep the same period of 40 years.

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**Cost of flood reduction scenarios**

Costs of the Flood Risk Reduction Scenario’s (costs in € .10 6)

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Incremental benefit Create in Excel a new table: called Flood Mitigation Scenario I ( see figure left). Column 1: Years ( starting with 1 up to 40 year) Column 2 Risk Reduction (i.e. Risk avoided, or Benefit) Column 3: Invest cost for the risk reduction scenario. Column 5: Maintenance Column 4: Incremental Benefits Enter the values and calculate the incremental benefit over the 40 years period.

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Net present value We need to take into account that the same amount of money in the future will be less valuable today. We will need therefore to calculate the so-called net present value (NPV)

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14 April 2017 Time value of money Money today is worth more than money in the future Why ? Inflation Risk Consumption Earning power (investment opportunities)

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**Compounding and Discounting**

14 April 2017 Compounding and Discounting Techniques for comparing values at different points in time In CBA mainly concerned with Discounting for better understanding first: Compounding

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**Compounding suppose amount of $ 100 on bank account interest 10%**

after 1 year ? After 2 and 3 years ?

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**Compounding start: 100 after 1 year: 100 + 10 = 110**

after 2 years: = 121 after 3 years: = 133.1 etc.

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**“what is the present value of a known future amount ?”**

14 April 2017 Discounting the reverse of compounding it looks from the future back to the present and asks: “what is the present value of a known future amount ?”

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14 April 2017 Discounting What is the present value of $ received at the end of 3 years from now, assuming an interest rate of 10% ?

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**Discounting in formula**

14 April 2017 Discounting in formula X0 = Xt / (1 + i)t X0 = present value Xt = value in year t

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**X0 ? Discounting - example X3 = 133.1; i = 0.10; t = 3**

14 April 2017 Discounting - example X3 = 133.1; i = 0.10; t = 3 X0 ? X0 = Xt / (1 + i)t X0 = / ( )3 X0 = / (1.331) = 100

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**Time Value of Money To care of time value of money**

We apply discount rates We discount each future annual amount

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**Flood mitigation Scenario I**

year incremental benefits NPV_10% 1 -8.333 -7.576 2 -6.887 3 -6.261 4 15.690 10.716 5 9.742 Until year 40

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**Flood mitigation Scenario II**

year incremental benefits NPV_10% 1 -8.333 -7.576 2 -6.887 3 -6.261 4 15.690 10.716 5 9.742 Until year 40

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**Internal Rate of Return (IRR)**

NPV decreases if i (interest rate) increases At one i (interest rate): =0 IRR

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**Internal rate of return**

Now we are going to calculate the Internal rate of return. The Internal Rate of Return is the discount rate/interest rate at which the NPV=0

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**NPV Scenario I and II at 10%**

Scenario I: $ * (negative !) Scenario II: $ * 106

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**IRR Scenario I and II at 10%**

Scenario II: %

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NPV and IRR

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NPV and IRR

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NPV and IRR

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**Summary CBA scenario I and II**

Flood Risk Reduction Scenario NPV at 5 % interest rate NPV at 10 % interest rate NPV at 20 % interest rate IRR Scenario I 42.23 -0.38 -14.96 9.91% Scenario II 203.80 93.69 27.79 42.32%

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Result Question: Which Mitigation Scenario would you advice the Municipality?

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**CBA -strengths Systematic way of thinking and analysis**

Focus on use of scarce resources Strong methodological basis Monetary measurement provides comparison Appeal to policy makers

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**Elements often overlooked in CBA in Natural Hazard and Disaster Management**

Indirect economic damage Social effects Irreplaceable items Stress induced by disaster Temporary evacuation Social disruption Environmental effects Evaluation of non-structural measures

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**Limitations Cost-Benefit Analysis**

One approach to assess the efficiency of (structural) risk reducing measures Take care of uncertainty of all parameters used Estimated values of objects at risk Probabilities of the hazard Take care of all aspects NOT considered: Social effects Irreplaceable items Stress induced by disaster Temporary evacuation Social disruption Environmental effects Indirect effects Discounting favours present generations One single outcome hides assumptions and value judgements

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